Some Series Sums

Click on the series whose solution you wants to get, you will be redirected to its solution

Series is one of the topic form Precalculus ,this this we find the sum of finite or infinite sequences. 

 

these question are generally asked in CSIR,NBHM,GATE,TIFR,IIT-JAM, and other Compitative exams,

In this post we are providing you some series and their solutions, you have to just click on the series who's solution you wants , you will be redirected to its solution.

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\(\displaystyle 1).\;\; \frac{1}{2}-\frac{1}{3\times 1!}+\frac{1}{4\times 2!}+\cdots\)

\(\displaystyle 2).\;\; \frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\cdots\)

\(\displaystyle 3).\;\; \frac{1}{2.3} +\frac{1}{4.5}+\frac{1}{6.7} +\cdots\)

\(\displaystyle 4).\;\; \frac{1}{3}+\frac{1}{4}.\frac{1}{2!} +\frac{1}{5}.\frac{1}{3!}+\cdots\)

\( \displaystyle 5).\;\; \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n(n+1)}\)

\( \displaystyle 6).\;\; \sum_{n=1}^{\infty} \frac{n^2-n+1}{n!}\)

\(\displaystyle 7).\;\; \frac{1}{5}+\frac{1}{3}.\frac{1}{5^3}+\frac{1}{5}.\frac{1}{5^5}+\cdots\)

\(\displaystyle 8).\;\; \frac{4}{20}+\frac{4.7}{20.30}+\frac{4.7.10}{20.30.40}+\cdots\)

\(\displaystyle 9).\;\; \sum_{n=0}^{\infty} \frac{5n+1}{(2n+1)!}\)

\(\displaystyle 10).\;\; \sum_{n=1}^{\infty} \frac{(-1)^n}{n(n+1)}\)

\(\displaystyle 11).\;\; \sum_{n=1}^{\infty} \frac{1}{(2n+1)^2}\)

\(\displaystyle 12).\;\; \frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+\cdots\)

\(\displaystyle 13).\;\; \sum_{n=1}^{\infty} \frac{1}{(2 n-1)^{2}}\)

\(\displaystyle 14).\;\; \sum_{n=1}^{\infty} n\left(\frac{1}{2}\right)^{n}\)

\(\displaystyle 15).\;\; \sum_{n=2}^{\infty} \frac{(-1)^{n}}{n^{2}+n - 2}\)

\(\displaystyle 16).\;\; \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\cdots+\frac{1}{100.101}\)

\(\displaystyle 17).\;\; \sum_{n=1}^{\infty}(-1)^{n+1} \frac{(n+1)^{2}+1}{(n+1) n !}\)

\(\displaystyle 18).\;\; \sum_{n=0}^{\infty} \frac{1}{(n+2) n!}\)